Solve for $x$ and $y$ using elimination. ${-x+5y = 30}$ ${x+4y = 33}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $9y = 63$ $\dfrac{9y}{{9}} = \dfrac{63}{{9}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-x+5y = 30}\thinspace$ to find $x$ ${-x + 5}{(7)}{= 30}$ $-x+35 = 30$ $-x+35{-35} = 30{-35}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 7}$ into $\thinspace {x+4y = 33}\thinspace$ and get the same answer for $x$ : ${x + 4}{(7)}{= 33}$ ${x = 5}$